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Aliases
Subgroups
3408 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 66 points:
(4,10,12,29,13,30,35,32)(6,20,22,52)(7,24)(8,27)(11,33,37,38,36,28,60,61)(14,42,40,31,41,63,62,64)(15,44,39,54,45,65,43,66)(17,34,46,59)(18,50)(19,47)(21,51,49,56)(23,57,48,53)(25,55)(26,58);(3,4,6,10,7,14,20,31,8,12,23,32,24,40,53,42,9,13,22,30,26,41,52,64,27,35,48,29,58,62,57,63)(5,15,17,44,18,11,34,38,19,39,49,66,50,37,51,33,16,45,46,65,25,36,59,61,47,43,21,54,55,60,56,28);(1,2);(3,5)(4,11,35,60,13,36,12,37)(6,21,22,49)(7,25)(8,19)(9,16)(10,28,32,38,30,33,29,61)(14,43,62,45,41,39,40,15)(17,48,46,23)(18,26)(20,51,52,56)(24,55)(27,47)(31,65,42,54,64,44,63,66)(34,53,59,57)(50,58);(5,16)(11,36)(15,45)(17,46)(18,25)(19,47)(21,49)(28,33)(34,59)(37,60)(38,61)(39,43)(44,65)(50,55)(51,56)(54,66)
Conjugacy classes & character table
164 conjugacy classes — view the full character table.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((4,10,12,29,13,30,35,32)(6,20,22,52)(7,24)(8,27)(11,33,37,38,36,28,60,61)(14,42,40,31,41,63,62,64)(15,44,39,54,45,65,43,66)(17,34,46,59)(18,50)(19,47)(21,51,49,56)(23,57,48,53)(25,55)(26,58), (3,4,6,10,7,14,20,31,8,12,23,32,24,40,53,42,9,13,22,30,26,41,52,64,27,35,48,29,58,62,57,63)(5,15,17,44,18,11,34,38,19,39,49,66,50,37,51,33,16,45,46,65,25,36,59,61,47,43,21,54,55,60,56,28), (1,2), (3,5)(4,11,35,60,13,36,12,37)(6,21,22,49)(7,25)(8,19)(9,16)(10,28,32,38,30,33,29,61)(14,43,62,45,41,39,40,15)(17,48,46,23)(18,26)(20,51,52,56)(24,55)(27,47)(31,65,42,54,64,44,63,66)(34,53,59,57)(50,58), (5,16)(11,36)(15,45)(17,46)(18,25)(19,47)(21,49)(28,33)(34,59)(37,60)(38,61)(39,43)(44,65)(50,55)(51,56)(54,66));
Finite Group Databasebeta